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Two-dimensional Stokes flows with cylinders and line singularities

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

J. M. Dorrepaal ,
M. E. O'Neill  and
K. B. Ranger
J. M. Dorrepaal
Affiliation:
Department of Mathematics, Old Dominion University, Norfolk, Virginia 23508, U.S.A.
M. E. O'Neill
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E 6BT
K. B. Ranger
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1.
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Abstract

A study is made of Stokes flows in which a line rotlet or stokeslet is in the presence of a circular cylinder in a viscous fluid. In contrast to the Stokes Paradox for flow past an isolated cylinder, it is shown that if either type of singularity, with suitably chosen strength and location, is present, there can exist a flow which is uniform at infinity. A similar phenomenon can occur when two equal cylinders rotate with equal and opposite angular velocities, and the flow pattern is then such that there is a closed streamline enclosing both cylinders.

MSC classification

Secondary: 76D99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 65 - 75
Copyright
Copyright © University College London 1984

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References

1.Jeffery, G. B.. The rotation of two circular cylinders in a viscous fluid. Proc. Roy. Soc. A, 101 (1922), 169.Google Scholar
2.Proudman, I. and Pearson, J. R. A.. Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid mech., 2 (1957), 237.CrossRefGoogle Scholar